{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Pair-distribution function\n",
    "\n",
    "The pair-distribution function describes the probability of finding a pair of atoms with a specific distance. We here describe how to compute a pair-distribution function  $g_2(r)$ of the type\n",
    "\n",
    "$$\n",
    "g_2(r) = \\frac{V}{N^2} \\left\\langle \\sum_{ij} \\frac{\\delta(r_{ij} - r)}{4\\pi r^2}  \\right\\rangle,\n",
    "$$\n",
    "\n",
    "where $V$ is the overall volume of the simulation cell and $N$ the total number of atoms (and hence $N/V$ is the number density of the system). The average $\\langle\\cdot\\rangle$ is an ensemble average. This pair-distribution function has the property $g_2(r)=1$ for $r\\to\\infty$.\n",
    "\n",
    "\n",
    "## Real-space\n",
    "\n",
    "The pair-distribution function above can be straightforwardly calculated from a neighbor list. We need to instruct the neighbor list to return the distance between atoms."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 4.0)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from ase.io import read\n",
    "from matscipy.neighbours import neighbour_list\n",
    "\n",
    "# Load a disordered configuration (amorphous carbon)\n",
    "a = read('../../tests/aC.cfg')\n",
    "\n",
    "# Get distance between atoms up to a distance of 5 Angstroms\n",
    "d = neighbour_list('d', a, cutoff=10.0)\n",
    "\n",
    "# Get distance distribution - we broaden the delta-function into finite sized shells\n",
    "n, x = np.histogram(d, bins=100, density=False)\n",
    "\n",
    "# Plot the pair-distribution function\n",
    "mean_distance = (x[1:] + x[:-1])/2\n",
    "mean_density = len(a) / a.get_volume()\n",
    "shell_volume = 4 * np.pi * (x[1:] ** 3 - x[:-1] ** 3) / 3\n",
    "plt.plot(mean_distance, n / (shell_volume * len(a) * mean_density))\n",
    "plt.xlabel('Distance $r$ (Å)')\n",
    "plt.ylabel('Pair-distribution function $g_2(r)$')\n",
    "plt.xlim(0, 10)\n",
    "plt.ylim(0, 4)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fourier space\n",
    "\n",
    "`matscipy` has utility function to compute pair-distribution (and other pair-correlation) functions. The utility function uses FFT to compute the long tail of the correlation function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 4.0)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matscipy.spatial_correlation_function import spatial_correlation_function\n",
    "\n",
    "n, x = spatial_correlation_function(a, [1]*len(a), approx_FFT_gridsize=0.1)\n",
    "\n",
    "plt.plot(x[x<10][1:], n[x<10][1:])\n",
    "plt.xlabel('Distance $r$ (Å)')\n",
    "plt.ylabel('Pair-distribution function $g_2(r)$')\n",
    "plt.xlim(0, 10)\n",
    "plt.ylim(0, 4)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.1"
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